Homogenization of non-autonomous convolution-type evolution equations.

The talk is devoted to the averaging problem for convolutional parabolic equations, whose coefficients oscillate rapidly in both spatial variables and time. It is assumed that the coefficients are periodic in space, and in time, they can be either periodic or random stationary. We will show that, if the second moment of the operator kernel is finite, the Cauchy problem for these equations admits averaging. We will also discuss possible types of convergence.